Optimize squaring operations

[andrewdalpino]

($a - $b) ** 2 in the hottest loops — confirmed at src/Kernels/Distance/Euclidean.php:47, plus SafeEuclidean, Cosine, SparseCosine, Minkowski, and the per-feature ** 2 in GMM (GaussianMixture), GaussianMLE, GaussianNB, Stats::variance. PHP ** goes through the generic pow() path. Replace with ($d = $a -$b); $d * $d. This is the single most-invoked path (KNN, ball/KD trees, seeding, GMM, FCM, KMeans, LOF). ~1.5–4× on distance-heavy workloads.

Benchmark	Before	After	Δ
Euclidean	5.981ms ±1.8%	3.395ms ±5.2%¹	−43% (1.76×)
SafeEuclidean	8.979ms ±3.0%	7.046ms ±9.9%¹	−22% (1.27×)
Cosine dense	11.134ms ±0.7%	5.572ms ±1.1%	−50% (2.00×)
Cosine sparse / very sparse	5.299 / 4.837ms	3.093 / 3.009ms	−42% / −38%
SparseCosine dense / sparse / very sparse	12.737 / 5.150 / 3.026ms	7.437 / 3.956 / 2.675ms	−42% / −23% / −12%
GaussianMLE train+predict	0.019s ±0.6%	0.015s ±1.9%	−21%
GaussianNB train+predict	0.026s ±1.0%	0.021s ±0.7%	−19%
GaussianMixture train+predict	0.116–0.147s ±28–33%	0.117–0.140s ±23–34%	inconclusive²

[Copilot]

Pull request overview

Optimizes repeated squaring in distance kernels, statistical calculations, and Gaussian model paths by replacing exponentiation with multiplication and cached deltas.

Changes:

• Optimizes Euclidean, cosine, and sparse distance calculations.
• Updates variance and Gaussian likelihood computations.
• Preserves review findings for arithmetic ordering and Minkowski scope.

Reviewed changes

Copilot reviewed 8 out of 8 changed files in this pull request and generated 2 comments.

Show a summary per file

File	Summary
src/Kernels/Distance/SparseCosine.php	Optimizes sparse vector norm calculations.
src/Kernels/Distance/SafeEuclidean.php	Optimizes NaN-safe squared differences.
src/Kernels/Distance/Euclidean.php	Optimizes squared distance calculations. Nit (3 votes): Minkowski is described as optimized but remains unchanged.
src/Kernels/Distance/Cosine.php	Optimizes vector norm calculations.
src/Helpers/Stats.php	Optimizes variance calculation.
src/Clusterers/GaussianMixture.php	Optimizes weighted variance and likelihood calculations. Moderate (3 votes): changed arithmetic ordering may alter underflow, overflow, and rounding behavior.
src/Classifiers/GaussianNB.php	Optimizes variance merging and likelihood calculations.
src/AnomalyDetectors/GaussianMLE.php	Optimizes variance merging and likelihood calculations.

---

💡 Add a code-review agent skill or configure MCP servers for context-aware, tailored reviews. Learn more in the docs.

[apphp]

Can we replace this with
$n * ($oldMean - $mean)
for better readability and it also 1 operation less? (x2 places)